Process control systems are used in numerous applications to regulate one or more parameters of a process. Most control systems are closed loop control systems in which information about a controlled variable is fed back to a controller to serve as the basis for control of one or more process variables. A signal representative of the controlled variable is compared by the controller with a preset desired value, or set point, of the controlled variable. If there is a difference, the controller produces an output such as to reduce the difference by manipulating one or more of the process variables. For example, the controlled variable might be the temperature of an effluent stream from a mixing tank; and the process variables might be the temperature and flow rates of the streams emptying into the tank as well as the speed of a mixer in the tank. If the temperature of the effluent is too low, the controller might open a little more a valve regulating the flow of one of the streams emptying into the tank or adjust the speed of the mixer.
Many linear-feedback control systems can be represented by the input-output relationship: ##EQU1## where C is the output, R is the set point, KG is the forward-loop transfer function, H is the feedback loop transfer function, and KGH is the open-loop transfer function.
For many processes it can be shown that the best controller is one which provides proportional, integral and derivative (PID) control. Proportional control of a first order process reduces the time constant of the system and the apparent gain of the process. However, it also introduces a deviation, or offset, between the time average of the controlled variable and the set point. This offset can be compensated for by providing for integral, or reset, control in addition to proportional control. Although the use of integral control tends to slow the response of the system, derivative control counters this by tending to anticipate where a process is going so that it can correct for the change in error. Ideally, the PID transfer function is given by the following equation: ##EQU2## where M is the manipulated variable, E is the error, K.sub.c is the controller gain, T.sub.i is the reset time and T.sub.d is the rate or derivative time. Each manufacturer of PID controllers typically uses a somewhat different transfer function. Numerous techniques are available to design or tune PID controllers to practical application. Details concerning many of these techniques are set forth in Section 22 of Perry & Chilton, Chemical Engineer's Handbook (McGraw Hill, 5th Ed. 1973).
Until quite recently most process controllers were analog devices because analog circuitry was the only cost effective way to build a single-loop controller. Such devices, however, could not easily be modified and could not execute complex control algorithms. As a result, they tended to be expensive and/or had limited capability.